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Let \(f(x)=\frac{1}{x}\) and \(g(x)=x^2\). Find the domain of \((f\circ g)(x)\).मान लीजिए \(f(x)=\frac{1}{x}\) और \(g(x)=x^2\) है। \((f\circ g)(x)\) का परिभाषा-क्षेत्र (domain) ज्ञात कीजिए।
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(\mathbb{R}\setminus\{0\}\)\(\mathbb{R}\setminus\{0\}\)
\((f\circ g)(x)=f(g(x))=f(x^2)=\frac{1}{x^2}\). This is defined only when the denominator is not zero, so \(x^2\ne 0\Rightarrow x\ne 0\). Hence the domain is \(\mathbb{R}\setminus\{0\}\).\((f\circ g)(x)=f(g(x))=f(x^2)=\frac{1}{x^2}\). यह तभी परिभाषित है जब हर (denominator) शून्य न हो, यानी \(x^2\ne 0\Rightarrow x\ne 0\). इसलिए परिभाषा-क्षेत्र \(\mathbb{R}\setminus\{0\}\) है।
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